Internal problem ID [9183]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1604.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-{\mathrm e}^{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.1 (sec). Leaf size: 23
dsolve(diff(diff(y(x),x),x)-exp(y(x))=0,y(x), singsol=all)
\[ y \relax (x ) = \ln \left (\frac {\tan ^{2}\left (\frac {c_{2}+x}{2 c_{1}}\right )+1}{2 c_{1}^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 26
DSolve[-E^y[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (-\frac {c_1}{1+\cosh \left (\sqrt {c_1} (x+c_2)\right )}\right ) \\ \end{align*}